Question

the four - sided geometric figure pictured is called a parallelogram. one feature of parallelograms is that opposite sides have equal lengths. the dotted line splits the parallelogram into two triangles. what is true about the congruency of the two triangles? the triangles are not congruent. the triangles can be proven congruent using sss. the triangles can be proven congruent using hl. more information is needed.

Explanation:

Step1: Recall parallelogram properties

Opposite sides of a parallelogram are equal. Let the parallelogram be \(ABCD\) with \(AB = CD\) and \(AD=BC\). The dotted line (diagonal) is common to both triangles.

Step2: Apply SSS congruence criterion

For two triangles \(\triangle ABC\) and \(\triangle ADC\) (formed by the diagonal), we have \(AB = CD\), \(AD = BC\), and the diagonal \(AC=AC\) (common side). By the SSS (Side - Side - Side) congruence criterion, \(\triangle ABC\cong\triangle ADC\).
HL (Hypotenuse - Leg) is for right - angled triangles (no information of right angles here). And we have enough information (from parallelogram properties and common side) to prove congruence.

Answer:

The triangles can be proven congruent using SSS.